9.5 Application of Pressure 9.5.3 eXtended Hydrostatic Compression Force Field (X-HCFF)9.6 Application of External Forces (EFEI)

9.5.4 Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP)

(July 14, 2022)

The Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP) method, which was introduced by Scheurer and co-workers, ¹⁰⁵⁸ Scheurer M. et al.
J. Chem. Theory Comput.
(2021), 17, pp. 583. Link overcomes the problems associated with the mechanochemical models of pressure, i.e. HCFF and X-HCFF. GOSTSHYP uses a uniform field of Gaussian potentials that is placed on the tessellated molecular surface and that compresses the electron density. Each Gaussian potential G ${}_{j}$ has the form

G_{j}=p_{j}\cdot\exp\left(-w_{j}(\textbf{r}-\textbf{r}_{0})^{2}\right)

(9.43)

During the GOSTSHYP routine, the parameters of the Gaussian potentials, $p_{j}$ and $w_{j}$ , are adjusted such that a user-defined pressure is applied. Atoms and molecules can be treated, and the pressure-induced increase in the electronic energy is physically sound. During the SCF, the energy expression takes the form

	$\displaystyle E_{\text{GOSTSHYP}}$	$\displaystyle=\sum_{j}E_{j}=\sum_{j}\int G_{j}(\textbf{r})\rho(\textbf{r})d% \textbf{r}$
		$\displaystyle=\sum_{j}\sum_{\mu,\nu}\sum_{a}\left<\chi_{\mu}\|G_{j}\|\chi_{\nu}% \right>c_{\mu a}^{*}c_{\nu a}$		(9.44)

Due to the availability of nuclear gradients, geometry optimizations under pressure using the GOSTSHYP model are possible. At present, GOSTSHYP is implemented at the SCF level, allowing calculations with Hartree-Fock and Density Functional Theory (DFT).

Example 9.15 Geometry optimization of cyclopentadiene and ethylene under a pressure of 40 GPa using the GOSTSHYP model

$molecule
   0 1
   C    1.1148422354   -0.6418674001    0.7279292386
   C    1.1148422354   -0.6418674001   -0.7279292386
   C    0.5936432126    0.5363396649    1.1772168767
   C   -2.0464511598   -0.6129291257    0.6711240568
   C   -2.0464511598   -0.6129291257   -0.6711240568
   C    0.5936432126    0.5363396649   -1.1772168767
   C    0.2915208637    1.4128825196    0.0000000000
   H    0.9756522868    2.2894492537    0.0000000000
   H   -0.7374232239    1.8214336422    0.0000000000
   H    1.4681344173   -1.4690333337   -1.3527755131
   H    1.4681344173   -1.4690333337    1.3527755131
   H   -2.3879086093    0.2541525765    1.2531118994
   H   -1.7231567891   -1.4887031107    1.2461940178
   H   -1.7231567891   -1.4887031107   -1.2461940178
   H   -2.3879086093    0.2541525765   -1.2531118994
   H    0.4773764265    0.8454441265    2.2200767812
   H    0.4773764265    0.8454441265   -2.2200767812
$end

$rem
   JOBTYPE               opt
   METHOD                pbe
   BASIS                 cc-pvdz
   GEOM_OPT_MAX_CYCLES   150
   SCF_ALGORITHM         diis_gdm
   MAX_SCF_CYCLES        150
   USE_LIBQINTS          1
   GEN_SCFMAN            1
   DISTORT               1
$end

$distort
   model                 gostshyp
   pressure              40000
   npoints_heavy         302
   npoints_hydrogen      302
   scaling               1.8
$end

Search Results

9.5.4 Gaussians On Surface Tesserae Simulate HYdrostatic Pressure (GOSTSHYP)